Received November 23, 2005, in final form March 20, 2006; Published online April 12, 2006

Abstract
We consider conditions for uniqueness of the solution of the Dirichlet or the Neumann problem for 2-dimensional wave
equation inside of bi-quadratic algebraic curve. We show that
the solution is non-trivial if and only if corresponding
Poncelet problem for two conics associated with the curve has periodic
trajectory and if and only if corresponding Pell-Abel equation has a solution.